Free oscillations of a cryogenic rotating fluid in a cylindrical cavity

Аuthors

Temnov A. N.^*, Shkapov P. M.^**, Yan Naing O. ^***

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: antt45@mail.ru
**e-mail: spm@bmstu.ru
***e-mail: yno64528@gmail.com

Abstract

This paper deals with the free oscillations of a rotating ideal cryogenic liquid inside a cylindrical tank with rigid walls. Cryogenic liquids are characterized by non-uniform temperature and density changes during operation and storage. The most significant stratification of the cryogenic component occurs in the direction of the external mass force field. To investigate the motion of this mechanical system, it is reasonable to use a stratified incompressible fluid model. The proposed work is devoted to the study of free oscillations of stratified fluid in a cylindrical tank, fully or partially filled with fluid rotating with small and large angular velocities. Calculations of eigenvalues of free oscillations of a rotating cryogenic liquid at a given buoyancy frequency for internal and surface waves in the form of graphs are given. In science, nature and various technical applications, rotating fluids occupy an important place. They are widely used in engineering, for example, in centrifuges, hollow shafts of liquid-cooled turbines and in stabilizing the rotation of rockets. Currently, there is a growing interest in the study of vibrations of cryogenic fluids filling finite-sized vessels used in various applications. The obtained results show that different types of waves can be observed in a rotating stratified fluid at both low and high rotational velocities, depending on the magnitude of the numbers  . The natural frequencies of these waves depend on the ratio of buoyancy forces and Coriolis inertia forces. The presence of stratification leads to an increase in the frequencies of free oscillations of the fluid for internal and surface waves. The study of oscillations of a rotating stratified fluid has shown that the spectrum of oscillation eigenvalues consists of two sets of real numbers: a two-index set   for surface waves (at low rotational velocity) and   (at high rotational velocity), and a three-index set   for internal waves.

Keywords:

free oscillations, cryogenic fluid, stratified fluid, internal waves, surface waves

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